Thermomechanical Buckling of Simply Supported Shallow FGM Spherical Shells with Temperature dependent Material

Document Type : Research Paper

Authors

1 Mechanical Engineering Department, Islamic Azad Univeristy, South Tehran Branch, Tehran, Iran

2 Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran

Abstract

The thermomechanical buckling of simply supported thin shallow spherical shells made of functionally graded material is presented in this paper. A metal-ceramic functionally graded shell with a power law distribution for volume fraction is considered, where its properties vary gradually through the shell thickness direction from pure metal on the inner surface to pure ceramic on the outer surface. The mechanical properties of the metal and ceramic are assumed to be temperature dependent. The governing equations are derived using the first-order shell theory of Love and Kirchhoff, the Donnell-Mushtari-Vlasov kinematics equations, and the calculus of variations. The analytical results are obtained for various types of loadings. The detailed results are compared and validated with the known data in the literature.

Keywords

Main Subjects


    [1]      Shen, H. S., “Thermal Postbuckling Behavior of Shear Deformable FGM Plates with Temperature-dependent Properties”, International Journal of Mechanical Sciences, Vol. 49, pp. 466-478, (2007).
 
    [2]      Yang, J., Liew, K. M., Wu, Y. F., and Kitipornchai, S., “Thermo-mechanical Post-buckling of FGM Cylindrical Panels with Temperature-dependent Properties”, International Journal of Solids and Structures, Vol. 43, pp. 307-324, (2006).
 
    [3]      Shahsiah, R., and Eslami, M. R., “Thermal Buckling of Functionally Graded Cylindrical Shells”, Journal of Thermal Stresses, Vol. 26, pp. 227-294, (2003).
 
    [4]      Shahsiah, R., and Eslami, M. R., “Functionally Graded Cylindrical Shell Thermal Instability Based on Improved Donnell Equations”, AIAA Journal, Vol. 41, No. 9, pp. 1819-1826, (2003).
 
    [5]      Sofiyev, A. H., “The Stability of Functionally Graded Truncated Conical Shells Subjected to Aperiodic Impulsive Loading”, International Journal of Solids and Structures, Vol. 41, pp. 3411-3424, (2004).
 
    [6]      Wu, L., Jiang Z., and Liu J., “Thermoelastic Stability of Functionally Graded Cylindrical Shells”, Composite Structures, Vol. 70, pp. 60-68, (2005).
 
    [7]      Sofiyev, A. H., “The Stability of Compositionally Graded Ceramic-metal Cylindrical Shells under Aperiodic Axial Impulsive Loading”, Composite Structures, Vol. 69, pp. 247-257, (2005).
 
    [8]      Bhangale, R. K., and Ganesan, N., “A Linear Thermoelastic Buckling Behavior of Functionally Graded Hemispherical Shell with a Cut-out at Apex in Thermal Environment”, International Journal of Structural Stability and Dynamics, Vol. 5, No. 2, pp. 185-215, (2005).
 
    [9]      Kadoli, R., and Ganesan, N., “Buckling and Free Vibration Analysis of Functionally Graded Cylindrical Shells Subjected to a Temperature-specified Boundary Condition”, Journal of Sound and Vibration, Vol. 289, pp. 450-480, (2006).
 
[10]      Sofiyev, A. H., “Thermoelastic Stability of Functionally Graded Truncated Conical Shells”, Composite Structure, Vol. 77, pp. 56-65, (2007).
 
[11]      Mirzavand, B., Eslami, M. R., and Shahsiah, R., “Effect of Imperfections of Thermal Buckling of Functionally Graded Cylindrical Shells”, AIAA Journal, Vol. 43, No. 9, pp. 2073-2076, (2005).
 
[12]      Bhangale, R. K., and Ganesan, N., “Linear Thermoelastic Buckling and Free Vibration Behavior of Functionally Graded Truncated Conical Shells”, Journal of Sound and Vibration, Vol. 292, pp. 341-371, (2006).
 
[13]      Mirzavand, B., Eslami, M. R., and Shahsiah, R., “Thermal Buckling of Imperfect Functionally Graded Cylindrical Shells Based on The Wan-Donnell Model”, Journal of Thermal Stresses, Vol. 29, No. 1, pp. 37-55, (2006).
 
[14]      Sofiyev, A. H., Deniz, A., Akcay, I. H., and Yusufoglu, E., “The Vibration and Stability of a Three-layered Conical Shell Containing an FGM Layer Subjected to Axial Compressive Load”, Acta Mechanica, Vol. 183, pp. 129-144, (2006).
 
[15]      Shahsiah, R., Eslami, M. R., and Naj, R., “Thermal Instability of Functionally Graded Shallow Spherical Shell”, Journal of Thermal Stresses, Vol. 29, No. 8, pp. 771-790, (2006).
 
[16]      Li, S. R. and Batra, R. C., “Buckling of Axially Compressed Thin Cylindrical Shells with Functionally Graded Middle Layer”, Thin-Walled Structures, Vol. 44, pp. 1039-1047, (2006).
[17]      Matsunaga, H., “Free Vibration and Stability of Functionally Graded Shallow Shells According to a 2D Higher-order Deformation Theory”, Composite Structures, Vol. 84, pp. 132-146, (2008).
 
[18]      Naj, R., Sabzikar Boroujerdy, M., and Eslami, M. R., “Thermal and Mechanical Instability of Functionally Graded Truncated Conical Shells”, Thin-Walled Structures, Vol. 46, pp. 65-78, (2008).
 
[19]      Sofiyev, A. H., Zerin, Z., and Korkmaz, A., “The Stability of a Thin Three-layered Composite Truncated Conical Shell Containing an FGM Layer Subjected to Non-Uniform Lateral Pressure”, Composite Structures, Vol. 85, pp. 105-115, (2008).
 
[20]      Mirzavand, B., and Eslami, M. R., “Thermal Buckling of Simply Supported Piezoelectric FGM Cylindrical Shells”, Journal of Thermal Stresses, Vol. 30, No. 11, pp. 1117-1135, (2007).
 
[21]      Sheng, G. G., and Wang, X., “Thermal Vibration, Buckling and Dynamic Stability of Functionally Graded Cylindrical Shells Embedded in an Elastic Medium”, Journal of Reinforced Plastics and Composites, Vol. 27, No. 2, pp. 117-134, (2008).
 
[22]      Najafizadeh, M. M., Hasani, A., and Khazaeinejad, P., “Mechanical Stability of Functionally Graded Stiffened Cylindrical Shells” Applied Mathematical Modeling, Vol. 33, pp. 1151-1157, (2009).
 
[23]      Naj, R., Sabzikar Boroujerdy, M., and Eslami, M. R., “Thermomechanical Instability of Functionally Graded Truncated Conical Shells with Temperature-dependent Material”, Journal of Strain Analysis, Vol. 43, pp. 259-272, (2008).
 
[24]      Sofiyev, A. H., “The Vibration and Stability Behavior of Freely Supported FGM Conical Shells Subjected to External Pressure”, Composite Structures, Vol. 89, No. 9, pp. 356-366, (2009).
 
[25]      Huang, H., and Han, Q., “Buckling of Imperfect Functionally Graded Cylindrical Shells under Axial Compression”, European Journal Mechanics A/Solids, Vol. 27, pp. 1026-1036, (2008).
 
[26]      Matsunaga, H., “Free Vibration and Stability of Functionally Graded Circular Cylindrical Shells According to a 2D Higher-order Deformation Theory”, Composite Structures, Vol. 88, pp. 519-531, (2009).
 
[27]      Sofiyev, A. H., Kuruoglu, N., and Turkmen, M., “Buckling of FGM Hybrid Truncated Conical Shells Subjected to Hydrostatic Pressure”, Thin-Walled Structures, Vol. 47, pp. 61-72, (2009).
 
[28]      Sofiyev, A. H., Aksogan, O., Schnack, E., and Avcar, M., “The Stability of a Three-Layered Composite Conical Shell Containing an FGM Layer Subjected to External Pressure”, Mechanics of Advanced Materials and Structures, Vol. 15, No. 6, pp. 461-466, (2008).
 
[29]      Huang, H., and Han, Q., “Nonlinear Buckling and Postbuckling of Heated Functionally Graded Cylindrical Shells under Combined Axial Compression and Radial Pressure,” International Journal of Nonlinear Mechanics, Vol. 44, No. 2, pp. 209-218, (2009).
 
[30]      Brush, D. O., and Almroth, B. O., “Buckling of Bars, Plates, and Shells,” McGraw-Hill, New York, (1975).
 
[31]      Eslami, M. R., Ghorbani, H. R., and Shakeri, M., “Thermoelastic Buckling of Thin Spherical Shells,” Journal of Thermal Stresses, Vol. 24, No. 12, pp. 1177-1198, (2001).
 
[32]      “ASME Boiler and Pressure Vessel Code”, Section II, American Society of Mechanical Engineers, New York, (2004).
 
[33]      Shackelford, J. F., and Alexander, W., “Materials Science and Engineering Handbook”, CRC Press, Boca Raton, Florida, (2001).
 
[34]      Hutchinson, J. W., “Imperfection Sensitivity of Externally Pressurized Spherical Shells”, Journal of Applied Mechanics, Vol. 34, pp. 49-55, (1967).